Workshop on New Materials for Renewable Energy October Non-equilibrium dynamics of photoinduced proton-coupled electron transfer

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1 Workshop on New Materials for Renewable Energy October 2011 Non-equilibrium dynamics of photoinduced proton-coupled electron transfer Alexander V. SOUDACKOV Dept. of Chemistry, Pennsylvania State University University Park U.S.A.

2 Theoretical Modeling of Proton- Coupled Electron Transfer Reactions in Energy Related Materials Alexander V. Soudackov Pennsylvania ns State University 1 WORKSHOP ON NEW MATERIALS FOR RENEWABLE ENERGY October 2011, ICTP, Miramare, Trieste, Italy

3 Sharon Hammes-Sciffer (SHS) Group Sarah Sharon Liz Edwards Hatcher Hammes- Irina Andrew Model Sirjoosingh Michelle PCET PCET studies Schiffer Navrotskaya Ludlow in Diabatization methods Os-complex lipoxygenase Anderson-Newns in Charulatha Jonathan Gold Skone PCET Hamiltonian electrode Venkataraman for PCET Electron-proton adiabaticity Interfacial PCET rate constants 2

4 Contributors Sharon Hammes- Schiffer Sarah Edwards Model PCET studies Michelle Ludlow Os-complex on Gold electrode Jonathan Skone Electron-proton adiabaticity Liz Hatcher PCET in lipoxygenase Irina Navrotskaya Anderson-Newns Hamiltonian for PCET Charulatha Venkataraman Interfacial PCET rate constants Andrew Sirjoosingh Diabatization tion methods in PCET 3

5 Random Facts about Penn State... Largest* alumni base in the world Total Alumni: 557,331 (165,182 registered) Notable alumni Paul Berg 48, 52g - Nobel Prize winner in Chemistry (1980): for his fundamental studies of the biochemistry of nucleic acids, with particular regard to recombinant-dna Jef Raskin 67g - credited with being the father of the Macintosh computer *unofficial and widely debated data 4

6 Motivation and relevance General model for PCET Electrochemical PCET Concluding remarks Outline four-state model and reduced two-state model vibronic free energy surfaces - generalized Marcus model Non-adiabatic PCET rate constant Fermi Golden Rule formulation Effects of proton donor-acceptor vibrational mode Free energy relationships and kinetic isotope effects Elecron-proton adiabaticity: HAT vs. PCET 5

7 Motivation PCET processes in energy related materials Photosynthesis Dye sensitized photoelectrochemical cell Thylakoid_membrane.png [Gagliardi et al., Coord. Chem. Rev., 254, 2459 (2010)] PT H O HO H Biomimetic systems (Nocera, Hammarström, Meyer) e - ET HN 3+ COOEt O N N hν ET Electrochemical PCET (Finklea) PT Os III (OH) + e - É Os II (OH) + H + + H + hν N N Ru III N N Os III (H 2 O) + e - É Os II (H 2 O) 6

8 Questions key-factors/properties affecting the rates? can we predict the trends in rates and kinetic isotope effects? can we provide interpretations of experimental data? can theory provide insights into fundamental mechanism? can we calculate PCET rate constants from first principles? 7

9 Questions key-factors/properties affecting the rates? can we predict the trends in rates and kinetic isotope effects? can we provide interpretations of experimental data? can theory provide insights into fundamental mechanism? can we calculate PCET rate constants from first principles? 8

10 General model for PCET 9

11 Four-state model for PCET Electron Donor Proton Donor (1a) H Proton Acceptor Electron Acceptor ET Electron Donor Proton Donor (2a) H Proton Acceptor Electron Acceptor Solvent Solvent PT EPT PT Electron Donor Proton Donor (1b) H Proton Acceptor Electron Acceptor ET Electron Donor Proton Donor (2b) H Proton Acceptor Electron Acceptor Solvent Solvent 10

12 2b, or not 2b: that is the William Shakespear ( ) Hamlet, Act III, Scene 1 11

13 Four-state model for PCET Gas phase vibronic Hamiltonian H 0 = T p + È U 1a (r p ) V PT V ET V EPT V PT U 1b (r p ) V EPT V ET V ET V EPT U 2 2a (r p ) V PT Í V EPT V ET V PT U Î 2 (r 2b p ) Vibronic states are obtained by diagonalizing the Hamiltonian in the appropriate electron-proton vibronic basis 12

14 Four-state model for PCET Vibronic Hamiltonian including interaction with the solvent H = T p + È U 1a (r p ) V PT V ET V EPT V PT U 1b (r p )+ z p V EPT V ET V ET V EPT U 2 (r 2a p )+ ze V PT Í V EPT V ET V PT U 2 (r 2b p )+ z p + z Î e Vibronic states are obtained by diagonalizing the Hamiltonian in the appropriate electron-proton vibronic basis 13

15 Four-state model for PCET H = T p + ET-blocks of the vibronic Hamiltonian V ET,V EPT = V PT È U 1a (r p ) V PT V ET V EPT V PT U 1b (r p )+ z p V EPT V ET V ET V EPT U 2 2a (r p )+ ze V PT Í V EPT V ET V PT U 2 (r 2b p )+ z p + z Î e Vibronic states are obtained by diagonalizing the Hamiltonian in the appropriate electron-proton vibronic basis 14

16 Reduction to two-state model Vibronic Hamiltonian with interaction for reduced two-state model È H 0 = T p + U I (r p,z p ) V el Í V el U II (r p,z p,z e ) Î Vibronic states are obtained by diagonalizing the Hamiltonian in the appropriate electron-proton vibronic basis 15

17 Reduction to two-state model 4 states: 1a, 1b, 2a, 2b 2a 1b 1a 2b proton coordinate 16

18 Reduction to two-state model 4 states: 1a, 1b, 2a, 2b 2a 1b 1a 2b proton coordinate 16

19 Reduction to two-state model two ET blocks: 1a/1b and 2a/2b 2a 1b 1a 2b proton coordinate 17

20 Reduction to two-state model two states: lowest 1a/1b and lowest 2a/2b I (1a/1b) II (2a/ Proton donor H Proton acceptor proton coordinate 18

21 Reduction to two-state model two states: lowest 1a/1b and lowest 2a/2b I (1a/1b) Proton donor j m H II (2a/ Proton acceptor proton coordinate 18

22 Reduction to two-state model two states: lowest 1a/1b and lowest 2a/2b I (1a/1b) II (2a/ Proton donor j m j n H Proton acceptor vibrational overlap proton coordinate V mn = ImĤ IIn ª V el S mn 18

23 Two-state model for concerted PCET limited to strong hydrogen bonds with highly asymmetric proton potentials Electron Donor Proton Donor H Proton Acceptor Electron Acceptor EPT Electron Donor Proton Donor H Proton Acceptor Electron Acceptor Solvent Solvent I = (1ab) II = (2ab) thermal reactions for majority of PCET systems exhibiting concerted EPT can be described in the framework of the two-state model non-equilibrium (photoinduced) PCET may require four-state model to properly describe proton vibrational relaxation 19

24 Interaction with polar solvent Vibronic free energy surfaces Generalized Marcus model (in terms of energy gap coordinate) solvent degrees of freedom adiabatically separated linear response approximation: quadratic dependence of self energy electron-proton vibronic Hamiltonian and its eigenstates parametrically depend on energy gap coordinate(s) U n (z,z p e)= S(z,z p e )+WW n (z,z p e ) free energy of n-th vibronic state quadratic self energy of solvent-solvent interactions vibronic energy including solute-solvent interaction (depends on reorganization energies) [Basilevsky, Chudinov, Newton, 1994; Soudackov, Hammes-Schiffer, 1999] 20

25 Interaction with polar solvent Vibronic free energy surfaces U n (z,z p e)= S(z,z p e )+WW n (z,z p e ) [Basilevsky, Chudinov, Newton, 1994; Soudackov, Hammes-Schiffer, 1999] 21

26 Marcus picture (vibronic model) reactant vibronic states {Im} {IIn} product vibronic states l mn o DG mn 22

27 Marcus picture (vibronic model) {Im} {IIn} reactant vibronic states l mn product vibronic states o DG mn k PCET = 2p h DG π mn Nonadiabatic (Golden rule) rate expression  m r Im  n -1/2 2 ( 4pl mn k B T ) Vmn exp È - D G π mn (k B T ) ÎÍ = (D G o mn + l mn ) 2 ; V 4l mn = Im Ĥ IIn ª V el S mn mn [ Soudackov and Hammes-Schiffer: J. Chem. Phys ] 22

28 Contributions of excited vibronic states Factors affecting relative contributions: Boltzmann populations of reactant states Free energy barriers Vibronic couplings (proton vibrational overlaps) 23

29 Effects of proton donor-acceptor vibrational Proton donor H Proton acceptor R Vibronic coupling (and overlap) depends strongly on R - can be approximated as a single exponential (Taylor expansion of the logarithm): V μν V 0 μν exp [ α μν (R R 0 )] V 0 μν V el S μν (R 0 ) [ Soudackov, Hatcher, and Hammes-Schiffer: J. Chem. Phys ] 24

30 Effects of proton donor-acceptor vibrational High-temperature (low frequency) limit: k PCET = 2p h  m P Im  n -1/2 ( 4pL mn k B T ) Vmn (R 0 ) 2 È exp 2a mn k B T È ÎÍ M W 2 exp - Î Í Low-temperature (high frequency) limit: k PCET = 2p h  m P Im mn = s + R + ; = mn R 2 W2 ; = h2 L l l l (a) 1 h 2 a l M 2 W dr 2 l (a) mn mn 2M  n ( Ω k B T ) ( Ω k B T ) È -1/2 ( 4pl s k B T ) Vmn (R 0 ) 2 exp l (a) mn - l È R hw - a mn dr exp - ÎÍ Í Î 2 ( DG 0 mn +L mn + 2a mn dr k B T ) 4L mn k B T ( DG 0 mn + l s ) 4l s k B T exact high-t low-t high-t exact low-t [ Soudackov, Hatcher, and Hammes-Schiffer: J. Chem. Phys ] 25

31 Applications System Experiment Theory Amidinium-carboxylate salt bridges Nocera JACS 1999 Iron bi-imidazoline complexes Mayer/Roth JACS 2001 Ruthenium polypyridyl complexes Meyer/Thorp JACS 2002 DNA-acrylamide complexes Sevilla JPCB 2002 Ruthenium-tyrosine complex Hammarström JACS 2003 Soybean lipoxygenase enzyme Klinman JACS 2004, Rhenium-tyrosine complex Nocera 2007 JACS 2007 Quinol oxidation Kramer JACS 2009 Osmium aquo complex/sam/gold Finklea JACS 2010 l d ET PT 26

32 Free energy relationship for PCET Excited vibrational states - NO INVERTED REGION! (at least for reasonable driving forces) [ Edwards, Soudackov, SHS, JPC A 2009; JPC B 113, (2009) ] 27

33 Free energy relationship for PCET What is a key difference between ET (with reorganizing intramolecular mode) and PCET with proton transferring ( reorganizing )? Overlap integrals ET: W = 400cm -1 ; dx =0.1Å PCET: W = 3000cm -1 ; dx =0.5Å However, inverted region in PCET is possible (blue curve) if proton donor-acceptor distance increases for more negative driving forces [ Edwards, Soudackov, SHS, JPC A 2009; JPC B 113, (2009) ] 28

34 Electron-Proton adiabaticity: HAT vs. Classification based on the vibronic coupling calculation? Georgievskii, Stuchebrukhov (2000): V DA = kv (ad) DA, k = 2pp exp ÎÍ plnp- p G(p +1) È Electronically non-adiabatic PT: p = t p t el = 1: V DA ÆV (na) DA = V el (I j ) (I I ) D j D [ p - adiabaticity parameter (semiclassical) ] Electronically adiabatic PT: p = t p t el? 1: V DA ÆV (ad) DA = D 2 [Skone, Soudackov, SHS, JACS 2006] 29

35 Electron-Proton adiabaticity: HAT vs. Ph- O- HL O & - Ph PCET t p = 0.098fs t el =7.60fs p = Ph- H C- CH 2 HL & 2 - Ph HAT t p =1.28fs t el =0.37fs p =3.45 [Skone, Soudackov, SHS, JACS 2006] 30

36 Electrochemical PCET 31

37 Electrochemical PCET Advantages of electrochemical PCET reaction can be easily controlled through the electrode potential measurements are performed using nondestructive techniques (e. g. cyclic voltammetry) measurable observables (current density) are directly related to the elementary act (no need to isolate the ET/PCET step) reactive species can be chemically attached to the electrode surface (e. g. via SAM) - fixed ET distance and no double layer effects realatively easy to measure kinetic isotope effects (KIE) - reliable probe for PC part in PCET 32

38 Electrochemical PCET: Concerted Model SC + M SC + + M [e (εm)] Solute complex with preformed hydrogen bonded PT interface (fast equilibrium with large Kassoc) Proton acceptor (A p) can be part of the redox species or a (buffer) molecule in solution f(ɛ Quasi-free electron model for the metal electrode m )= [ 1+e βɛ ] 1 m Significantly different asymmetric proton potentials for reduced and oxidized forms of the solute complex [ Venkataraman, Soudackov, Hammes-Schiffer: J. Phys. Chem. C 2008 ] 33

39 Electrochemical PCET: nonadiabatic Im IIn l mn o DG mn 34

40 Electrochemical PCET: nonadiabatic Im IIn l mn o DG mn SC SC + + e (M) Conduction band ɛ μ M ΔU + μ M e(φ M φ s ) Solvent coordinate 34

41 Electrochemical PCET: nonadiabatic SC SC + + e (M) Conduction band ɛ μ M ΔU + μ M e(φ M φ s ) Solvent coordinate Vibronic couplings at equilibrium donor-acceptor distance R0 for the reduced complex: V mn 0 (x,e)ª V el (x,e)s mn (R 0 ) Free energy differences: DG mn (x,e)= DU mn + k B T ln Q II Q I + e- e[h - f s (x)] overpotential electronic level in the metal 34

42 Electrochemical PCET: nonadiabatic Oxidation (anodic) and reduction (cathodic) transition probabilities: W SC ÆM (x,e)= 1 P h m V 0 mn (x,e) 2 È exp 2k B Ta 2 mn p Â Î Í M W 2 m,n k B T L mn È ( DG mn (x,e)+ L mn +2k Ta 2 exp - k B mn dr ) 4k B T L mn ÎÍ W MÆSC + (x,e)= 1 P h m V 0 mn (x,e) 2 È exp 2k B Ta 2 mn - 2a M W 2 mn dr p  m,n Î Í k B T L mn È (-DG mn (x,e)+ L mn Ta 2 - exp - 2 2k B mn dr ) 4k B T L mn ÎÍ R 0 I Reduced solute complex: A e $ D p H A p R 0 II dr = R 0 II - R 0 I Oxidized solute complex: A e D p H A p 35

43 Electrochemical PCET: rate constants SC SC + + e (M) Conduction band ɛ μ M ΔU + μ M e(φ M φ s ) Solvent coordinate Fermi distribution x-dependent anodic and cathodic first order rate constants: k a (x)= k c (x)= Ú Ú de[1- f(e)]r(e)w SCÆM (x,e) def(e)r(e)w MÆSC + (x,e) In the vicinity of the Fermi level: r(e)v el (x,e) 2 ª r(e F )V el (x,e F ) 2 36

44 Electrochemical PCET: current densities Exponential dependence of the coupling on the distance x to the electrode surface (for nonadiabatic ET β 1 Å -1 ) Gouy-Chapman-Stern model: low electrolyte concentrations, large Debye length (β κ) - current is dominated by PCET at the outer ψ - potential at outer Helmhotz plane METAL + IHP OHP SOLUTION φ m φ H o φ S COMPACT C LAYER DIFFUSE LAYER j a (h)= F Ú dxc SC (x)k a (x,h)ª FC k a (x H,h) SC b x H Ú j c (h)= F dxc SC + (x)k c (x,h)ª FC SC + x H k c (x H,h) b e - zbey e -(z+1)bey [ Venkataraman, Soudackov, Hammes-Schiffer: J. Phys. Chem. C 2008 ] 37

45 Electrochemical PCET: current densities For redox species chemically attached to SAM on the electrode R SAM j a (h)= ec cov SC (R SAM ) k a (R SAM,h) j c (h)= ec cov (R SC + SAM ) k c (R SAM,h) 38

46 Electrochemical PCET: transfer defined via logarithmic derivative of the cathodic current density a PCET (h)= - 1 d ln j c (h) k B T d(eh) approximate expression (ignore the effects of the excited vibronic states) (assume that electron transfers only to/from the Fermi level) a PCET (h)ª k B Ta 00 dr + eh L 2L 39

47 Electrochemical PCET: transfer defined via logarithmic derivative of the cathodic current density a PCET (h)= - 1 d ln j c (h) k B T d(eh) approximate expression (ignore the effects of the excited vibronic states) (assume that electron transfers only to/from the Fermi level) R 0 I a PCET (h)ª 1 2 Ta - k dr eh B L 2L $ A e D p H A p II R 0 A e D p H A p dr = R 0 II - R 0 I deviation from standard value of 1/2: due to different equilibrium proton donor-acceptor distances in reduced and oxidized solute 39

48 Electrochemical PCET: main features Observable kinetic isotope effects (KIE) (up to ~4 reported) Different effective temperature dependent activation energies for cathodic and anodic processes ±2k B Tα(terms μν δr on the order of a few kcal/ mol) δr =0 δr =0.05 Å transfer coefficient deviates from 0.5: α PCET (η) 1 2 α 00δR + eη βλ 00 βλ 00 2Λ 00 40

49 Electrochemical PCET: application [Os II (bpy)2(4-aminomethylpyridine)(h2o)] 2+ attached to a mixed self-assembled monolayer on a gold electrode Experimental data [ Madhiri, Finklea: Langmuir 2006 ] Os III (OH) + e - + H + É Os II (OH) + H + Os III (H 2 O) + e - É Os II (H 2 O) 41

50 Electrochemical PCET: application [Os II (bpy)2(4-aminomethylpyridine)(h2o)] 2+ attached to a mixed self-assembled monolayer on a gold electrode Experimental data [ Madhiri, Finklea: Langmuir 2006 ] concerted PCET mechanism (data incompatible with the stepwise model) Os III (OH) + e - + H + É Os II (OH) + H + Os III (H 2 O) + e - É Os II (H 2 O) 41

51 Electrochemical PCET: application [Os II (bpy)2(4-aminomethylpyridine)(h2o)] 2+ attached to a mixed self-assembled monolayer on a gold electrode Experimental data [ Madhiri, Finklea: Langmuir 2006 ] concerted PCET mechanism (data incompatible with the stepwise model) Kinetic isotope effect KIE 2 at ph ~ 4 proton acceptor: COO group (SAM) with pka 5 asymmetric Tafel plot with higher anodic currents (suggested two different reorganization energies for cathodic and anodic processes) Os III (OH) + e - + H + É Os II (OH) + H + Os III (H 2 O) + e - É Os II (H 2 O) 41

52 Electrochemical PCET: application [Os II (bpy)2(4-aminomethylpyridine)(h2o)] 2+ attached to a mixed self-assembled monolayer on a gold electrode Experimental data [ Madhiri, Finklea: Langmuir 2006 ] concerted PCET mechanism (data incompatible with the stepwise model) Kinetic isotope effect KIE 2 at ph ~ 4 proton acceptor: COO group (SAM) with pka 5 asymmetric Tafel plot with higher anodic currents (suggested two different reorganization energies for cathodic and anodic processes) Observed strong potential dependence of the transfer coefficient ( ) (non-linear free energy relationship): α(0) = 0.46 ± Os III (OH) + e - + H + É Os II (OH) + H + Os III (H 2 O) + e - É Os II (H 2 O) 41

53 Electrochemical PCET: application Theoretical modeling: input parameters DFT (B3LYP) calculations of optimized geometries and proton profiles for reduced and oxidized Os complexes: δro-o = +0.17Å (reduced: 2.49Å and oxidized: 2.66Å) proton vibrational wavefunctions generated using Fourier Grid Hamiltonian method R δr = +0.17Å Os(II) Os(III) solvent SAM metal S 00 (H ) = 0.44 a 00 (H) = 6.02Å -1 [ Liu, Newton, 1994 ] [ Ludlow, Soudackov, Hammes-Schiffer: JACS 2010 ] 42

54 Electrochemical PCET: application Theoretical modeling: no fitting to experimental data! reproduced asymmetric Tafel plot calculated transfer coefficient α(0) = 0.47 (c.f. experimental value of 0.46 ± 0.02) Experiment (ks = 0.92 s -1 ) Theory a PCET (0) ª 1 2 Ta - k dr B 00 0 L calculated KIE for the standard rate constant: KIE ~ 2.0 (c.f. experim. value of KIE ~ 2) ruled out H2O as proton acceptor: δr < 0 [ Ludlow, Soudackov, Hammes-Schiffer: JACS 2010 ] 43

55 Conclusions Simple four-state model (1a-1b-2a-2b) describes essential physics of PCET processes can also describe all possible fundamental mechanisms (next talk) Majority of concerted PCET reactions are vibronically nonadiabatic Electron-proton adiabaticity parameter can be used to distinguish HAT (electronically adiabatic PT) and PCET (electronically non-adiabatic PT) Proton donor-acceptor vibrational motion has important effects on the rates and isotope effects Model can explain (and predict?) trends in rates and isotope effects PCET in polar solvents electrochemical PCET Photoinduced PCET dynamics! 44

56 Financial support Acknowledgements NSF AFOSR NIH NSF Center for Chemical Innovation (CCI) 45

57 Thank you! 46